Another part of the \(H_0-r_d\)  puzzle is the effect of the matter energy density \(\Omega _m\) . A comparison of different results for \(\Omega _m\)  can be seen on Fig. 1 b), where we have plotted the \(H_0-\Omega _m\)  plane. Note that the eBOSS points used here are different from the ones used in Table 2, as we use different set of published points (Table 4 in Ref. [1]}). Also, we add the points by ACT which can be found in Table 4 in Ref. [2]}. Our points are once again in green and as we can see they fit very close to Plancks's results in blue which come with very small error on \(H_0\)  but rather large on \(\Omega _m\)  (\(\Omega _m^{Planck}=.289,0\pm 0.03\) ). In our case, the matter density is lower than the expected. One can also note that removing the top right point (belonging to BAO +BBN+H0LiCOW, see Table 2) will make the points along with the error bars to lie on approximately one plane, similar to the one in the \(H_0-r_d\)  plane and thus hinting at possible degeneracy (in orange and yellow respectively). This has been commented already in [3]} and is related to the fact we do not know how exactly the phase space of all parameters looks like. The tension for \(H_0-r_d-\Omega _m\)  appears in different measurements (Planck, BAO, ACT etc), some from the early Universe, others from the late one and the independent local measurements. This once again poses the question whether we need to consider the full parameter space when discussing the tension.
<FIGURE>